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Time Dilation Formula
The difference in time between two events measured by moving in relation to one another or by gravitational mass or masses at various locations is known as time dilation, according to the theory of relativity.
Think about a clock that has two observers. While one observer is moving at the speed of light, the other is stationary. Time dilation is the existence of a time difference between the two clocks.
The Extramarks website and mobile app both have comprehensive explanations of the Time Dilation Formula for students to view. These solutions, which are based on the Time Dilation Formula, make it simple for students to comprehend the ideas. All necessary formulas in the solutions to the Time Dilation Formula have been highlighted and mentioned in the article so that students can locate them quickly and easily without wasting any time. These notes on the Time Dilation Formula, which are accessible via the Extramarks website and mobile application, will provide answers to students’ inquiries. For board exams, the notes on the Time Dilation Formula are very helpful because they can help students solidify their foundations. The article has successfully used examples to show how important the Time Dilation Formula is.
What is Time Dilation?
Time dilation is a phenomenon in which two bodies that are moving in relation to one another—or even just having different gravitational fields from one another—experience time moving at different rates.
It alludes to a special circumstance in which time can advance at various rates depending on the reference frame. It also depends on how quickly different reference frames move relative to one another. The measurement of elapsed time using two clocks is known as time dilation in layman’s terms. Additionally, two reference frames are the appropriate time (oneposition time) and observer time (twoposition time). Furthermore, because they are connected, we can calculate the time dilation of one by knowing the speed and velocity of the others.
Students enrolled in various boards of education can also access the Time Dilation Formula notes in Hindi. The notes for the Time Dilation Formula were written and organised with students in mind, and the framework is very easy to understand. While taking notes for yourself, you can review these answers to the Time Dilation Formula. Students find the Time Dilation Formula to be very appealing because it has a diverse, dynamic, and varied nature.
In order to assuage concerns about accuracy, the Hindi translation of the Time Dilation Formula was produced in collaboration with some of Extramarks’ best and most knowledgeable translators. The Time Dilation Formula notes include all the necessary stepbystep calculations. These Time Dilation Formula notes are available for download so that you can study independently.
Formula for Time Dilation
The Time Dilation Formula is given by,
T =T0 /√1−(v2/c2)
where,
T is the time observed
T0 is the time observed at rest v is the velocity of the object
c is the velocity of light in a vacuum (3 × 108 m/s2)
Derivation of Time Dilation
We can link the distances into each other and then calculate each distance in terms of the pulse’s time of travel in the relevant reference frame in order to quantitatively compare the time measurements in the two inertial frames. After that, the resulting equation can be solved for T using T0.
The hypotenuse of a right triangle is made up of the lengths D and L. According to the Pythagorean theorem, s2 = D2 + L2.
The light pulse and the spacecraft have travelled 2s and 2L, respectively, in time in the observer’s frame who is on earth. The length D is the distance covered by the light pulse in time T0 in the astronaut’s frame. As a result, we have three equations to consider:
2L = vT, 2D = cT0, and 2s = cT
We used Einstein’s second postulate by assuming the speed of light to be c in both inertial frames. Now, we can incorporate these findings into the Pythagorean theorem’s initial formulation:
s2 = D2+ L2
(c × T/2)2 = (c × T0/2)2 + (v × T/2)2
Then we rearrange to obtain
(c × T)2 – (v × T)2 = (c × T0)2
Finally, solving for T in terms of T0 gives us
T =T0 /√1−(v/c)2
This is equivalent to
T = γT0,
where γ is the relativistic factor (often called the Lorentz factor) given by
γ =1/√1−(v2/c2)
and v and c are the speeds of the moving observer and light, respectively.
Sample Problems
Problem 1: Determine the relativistic time, if T0 is 7 years and the velocity of the object is 0.55c.
Solution:
Given:
T0 = 7 years
v = 0.55c
The Formula for time dilation is given by,
T =T0 /√1−(v2/c2)
T = 7/√1(0.55)2(32 x 1016)/32 x 1016
T = 7/√1 (0.55)2
T=7/0.8351
T = 8.38 years